Swags again - water aspects

I've been hosing down my new swag in order to waterproof it, according to the instructions. Actually the Melbourne weather has been doing most of the work for me today.

I put a blue tarp, which is larger than the swag, underneath it before the soaking exercise commenced so water has fallen on the tarp and flowed under the swag where, no doubt, it has pooled. Now as the tarp is (more or less) waterproof but the underside of the swag is canvas and will absorb water (I assume?) does this mean those pools of water will, eventually, soak through into my bedding?

If that is the case, is it better to put the swag directly onto the ground without the tarp underneath?

Mike Harding